WASHINGTON — There is growing concern in Congress about the impact of a new law that makes a balanced budget mandatory by 1991, with supporters and opponents fearing the measure could lead to deep and drastic cuts in domestic social and defense spending.

The roll call for passage of the Gramm-Rudman budget-balancing bill had barely begun Wednesday night when one of its chief architects, Sen. Pete Domenici, R-N.M., bluntly told reporters the legislation would lead to chaos.

``I think there is a substantial chance of disarray, disorder, confusion and confrontation,`` said Domenici, chairman of the Senate Budget Committee.

But, said the senator, ``so be it,`` because the chaos could force the ``big players`` to sit down and make the painful political and policy decisions necessary to meet the deficit targets mandated by Gramm-Rudman.

Among the decisions, Domenici said, are those on the size of the reductions in defense spending and whether there will have to be a tax increase.

The senator, who took over much of the reponsibility for writing the law because of his expertise on the federal budget, may be one of the few people on Capitol Hill or in the White House who has any idea of how the bill actually will work.

The legislation, which was approved by large bipartisan majorities, is aimed at balancing the budget by fiscal 1991 through a process of automatic spending cuts that would be triggered if Congress and the president fail to meet annual deficit goals.

The bill passed Congress with the endorsement of President Reagan because Congress and the president have been unable to do much about the deficit except watch it grow for the last few years, and it gave them an opportunity to appear to be taking action.

But reality will rear its unattractive head next month when spending for fiscal 1986 will have to be cut $11.7 billion, and the president will have to submit a fiscal 1987 budget calling for more than $50 billion in reductions.

The effect of the spending cuts ``is going to come as a shock to a bunch of people who voted for this,`` Domenici said.

Defense and domestic spending for 1986 will have to be cut equally even as Congress is still trying to implement savings it voted months ago as part of the budget resolution.

The reduction in defense will have to be more than $5 billion in outlays, which translates into more than $15 billion in budget authority, according to Sen. Sam Nunn, D-Ga., the ranking member of the Senate Armed Services Committee, who voted for the bill even though he realizes what is going to happen.

``This would ... represent negative growth in national defense budget authority of 7 to 9 percent,`` Nunn said in a speech on the Senate floor.